Invited Lecture
Simulating deformable objects: a numerical perspective
Computer Science, UBC, Vancouver, Canada
Abstract
The problem of effectively and efficiently simulating the constrained motion of deformable objects in 3D is ubiquitous in robotics, computer animation, control and fabrication. I will examine a variety of numerical methods that arise in this context. The goals and merits of suitable numerical algorithms for these applications are different from those of typical numerical analysis research in dynamical systems. Here the mathematical model is not completely fixed a priori but must be adjusted as necessary to capture desired behaviour, with an emphasis on effectively producing lively animations of objects with complex geometries. Results are often judged by realistic appearance and flexibility as well as the efficacy of the numerical procedures employed. Contact and friction forces that arise in a constrained motion can add significant difficulty. And yet, we show that numerical mathematics can contribute significantly to the development of appropriate methods and their analysis in a variety of areas including finite element methods, stiff and highly oscillatory ODEs, model reduction, and constrained optimization.